# Calculate the average force acting on the block

## Homework Statement

A block of mass 2 kg starts from rest and begins to move at time t=0 along a straight line on a smooth horizontal surface. The displacement of the block, s, depends on time, t, given by s=3+2t+t^3 . t is expressed in second and s in meter. Calculate the average force acting on the block during the first 3 seconds of its motion. Express your answer in Newton.

F=ma

## The Attempt at a Solution

To find avg force , I'll need to find avg acceleration and then multiply it with mass of block.
But the problem is I don't know how to calculate avg acceleration from displacement as a function of time . Please Help.

Last edited:

Related Introductory Physics Homework Help News on Phys.org
What is the definition of average acceleration?

What is the definition of average acceleration?
Avg acceleration = v-u/t

collinsmark
Homework Helper
Gold Member
Is this a calculus based physics class?

What's the relationship between instantaneous velocity and instantaneous displacement?

haruspex
Homework Helper
Gold Member
Avg acceleration = v-u/t
(v-u)/t, yes. You know u; how will you calculate v? (See collinsmark's hint.)

(v-u)/t, yes. You know u; how will you calculate v? (See collinsmark's hint.)
Instantaneous velocity is derivative of displacement, so v= 2+3t^2
so at the third second v= 2+3*9=29 .
But there are 2 problems , first when I substitute 0 for t I get v=2 But they told us that the object starts from rest ! Also I'm probably not supposed to use calculus . ( Its OK if I have to , but if there is a way without calculus then it is preferred .)

collinsmark
Homework Helper
Gold Member
Instantaneous velocity is derivative of displacement, so v= 2+3t^2
so at the third second v= 2+3*9=29 .
That looks right.

But there are 2 problems , first when I substitute 0 for t I get v=2 But they told us that the object starts from rest !
That is a good point.

You might want to check to make sure the equation was typed in/written down correctly. Either something is wrong with the s = 3 + 2t + t3, or something is wrong with the statement that the object starts from rest (with the object beginning to move at time t = 0). One way or the other, something is wrong with the problem statement.

Also I'm probably not supposed to use calculus . ( Its OK if I have to , but if there is a way without calculus then it is preferred .)
Calculus or no calculus, it doesn't change the fact that the object has a velocity of 2 m/s at time t = 0, if we are to believe the
s = 3 + 2t + t3 equation. Using a non-calculus method won't change that fact. Calculus makes doing physics problems easier, but it doesn't change any results.

[Edit: One way out of this (sort of) is if the object was hit with an impulse at time t = 0, such that there was infinite force applied over an infinitesimal interval of time, and the area of the impulse is finite (kind of like a baseball being hit with a baseball bat). With this, you can still calculate the average force from time t = 0 to time t = 3, and the result will be finite. But you will get different answers depending on whether you start at 0+ vs. 0-. So something still looks fishy to me in the problem statement.]

Last edited:
That looks right.

That is a good point.

You might want to check to make sure the equation was typed in/written down correctly. Either something is wrong with the s = 3 + 2t + t3, or something is wrong with the statement that the object starts from rest (with the object beginning to move at time t = 0). One way or the other, something is wrong with the problem statement.

Calculus or no calculus, it doesn't change the fact that the object has a velocity of 2 m/s at time t = 0, if we are to believe the
s = 3 + 2t + t3 equation. Using a non-calculus method won't change that fact. Calculus makes doing physics problems easier, but it doesn't change any results.

[Edit: One way out of this (sort of) is if the object was hit with an impulse at time t = 0, such that there was infinite force applied over an infinitesimal interval of time, and the area of the impulse is finite (kind of like a baseball being hit with a baseball bat). With this, you can still calculate the average force from time t = 0 to time t = 3, and the result will be finite. But you will get different answers depending on whether you start at 0+ vs. 0-. So something still looks fishy to me in the problem statement.]
Maybe the velocity at t=0 is really 2 because when I reread the question , I realised that they say the object starts from rest BUT starts to move at t=0. So lets suppose that v=2 at t=0 .
Then acceleration (avg) =29-2/3=9.
So avg force = 18 , right ? But the answer sheet says that the correct answer is 16.
Am I wrong or is the answer sheet wrong? Please tell quickly .

Sounds way too cryptic for something that ought to be easy. Most likely, a mistake in the formulation.

haruspex
Homework Helper
Gold Member
I tried to figure out what the mistake is in the question. To resolve the initial speed paradox, need to get rid of the linear term, 2t, in the s equation. Maybe 2t^2? That gives 26 as the answer. Two typos in one question?

I tried to figure out what the mistake is in the question. To resolve the initial speed paradox, need to get rid of the linear term, 2t, in the s equation. Maybe 2t^2? That gives 26 as the answer. Two typos in one question?
Forget about that , lets suppose the object doesn't start from rest (but with v=2) .

collinsmark
Homework Helper
Gold Member
Forget about that , lets suppose the object doesn't start from rest (but with v=2) .