How Does Acceleration Affect Velocity and Position in Kinematics?

[Spartan029]

Hello everyone. I am stumped here with this problem, i feel like it should be fairly simple but i can't seem to figure it out.

Homework Statement

If the acceleration for a given object is given by the function:

a(t) = +(3 m/s^3) · t
(Note: units are included in the eqn, so if [t]=s then [a]=m/s^2.)

(a) Examining this function, you can tell that:
a1)the size of the acceleration will: ?
a2)the direction of the acceleration will be: ?

(b) If vi (at t=0 s) is -3 m/s, find v(t). Then answer the below:
(b1)the size of the velocity will: ?
(b2)the direction of the velocity will be: ?

(c) If xi (at t=0 s) is -7 m, find x(t). Then answer the below:
c1)After 4 s have passed, What position (x) is the object at now? ___m
c2)What is the total distance traveled (since t=0 s)? ___m

Homework Equations

I really don't know, Integration? maybe

The Attempt at a Solution

Okay so for part (a) I answered that the size would be "increasing" which is correct. Also the direction of the acceleration will be "in the + direction" which is aslo correct.
So for part (b) i take the integral of the a(t) and get:

v(t) = (3/2)t^2 - 3 m/s

by examining this i answered that the size would be "increasing" and "in the + direction" both of my answers are wrong and i don't understand why.

Okay so i skip to part (c) take the integral of v(t):

x(t) = (1/2)t^3 - 3t - 7 m

so
x(4) = (1/2)(4^3) - 3(4) - 7 = -11

-11 was not correct. so i thought it wise not to go on to part c2) lol

and here i am stumped. Any help would be much appreciated. Thanks!

 

[alphysicist]

Hi Spartan029,

Hello everyone. I am stumped here with this problem, i feel like it should be fairly simple but i can't seem to figure it out.

Homework Statement

If the acceleration for a given object is given by the function:

a(t) = +(3 m/s^3) · t
(Note: units are included in the eqn, so if [t]=s then [a]=m/s^2.)

(a) Examining this function, you can tell that:
a1)the size of the acceleration will: ?
a2)the direction of the acceleration will be: ?

(b) If vi (at t=0 s) is -3 m/s, find v(t). Then answer the below:
(b1)the size of the velocity will: ?
(b2)the direction of the velocity will be: ?

(c) If xi (at t=0 s) is -7 m, find x(t). Then answer the below:
c1)After 4 s have passed, What position (x) is the object at now? ___m
c2)What is the total distance traveled (since t=0 s)? ___m

Homework Equations

I really don't know, Integration? maybe

The Attempt at a Solution

Okay so for part (a) I answered that the size would be "increasing" which is correct. Also the direction of the acceleration will be "in the + direction" which is aslo correct.
So for part (b) i take the integral of the a(t) and get:

v(t) = (3/2)t^2 - 3 m/s

by examining this i answered that the size would be "increasing" and "in the + direction" both of my answers are wrong and i don't understand why.

Okay so i skip to part (c) take the integral of v(t):

x(t) = (1/2)t^3 - 3t - 7 m

so
x(4) = (1/2)(4^3) - 3(4) - 7 = -11

I think you squared the 4 instead of cubing it.

 

[Spartan029]

Hi Spartan029,



I think you squared the 4 instead of cubing it.

lol, yea i messed up there, thanks for pointing it out.

I figured out how to solve the problem thanks for helping me!

 

[alphysicist]

Sure, glad to help!