Solving for Distance, Velocity and Acceleration

In summary, by substituting t=5 into the given equations, we can calculate the distance, velocity, and acceleration as 22.17m, 8.867m/s, and 3.547 m2/s respectively. It is important to note that the time constant should include units to ensure dimensional consistency.
  • #1
jenny121
2
3
Homework Statement
The distance moved by a mass is related to the time by x=3e^(0.4t) m. Find the following value after 5 sec
Relevant Equations
x=3e^(0.4t)
Distance:
substitute t=5 into x=3e^(0.4t)
22.17m

Velocity:
v=dx/dt
=1.2e^0.4t____(1)
Sub t=5 back into (1)
v= 8.867m/s

Acceleration:
a=dV/dt
=0.48e^0.4t____(2)
sub t=5 back into (2)
a= 3.547 m2/s

I am not sure if i am doing this right on dx/dt and dv/dt
 
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  • #2
Your calculus looks fine. You might question the dimensional aspects of these equations, which the problem setter has chosen to ignore.
 
  • #3
PeroK said:
Your calculus looks fine. You might question the dimensional aspects of these equations, which the problem setter has chosen to ignore.
It can be fixed by giving the time constant a unit:
##x=(3m)e^{(0.4s^{-1})t}##.
Those units then flow through to the answer.
 
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  • #4
I see, thanks. after putting the unit it makes more sense now
 
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Related to Solving for Distance, Velocity and Acceleration

1. How do you calculate distance?

To calculate distance, you can use the formula: distance = velocity x time. This means that the distance an object travels is equal to its velocity (speed) multiplied by the time it takes to travel that distance.

2. What is the difference between velocity and speed?

Velocity and speed are often used interchangeably, but they have different definitions in physics. Velocity is a vector quantity that includes both the speed and direction of an object's motion, while speed is a scalar quantity that only represents the magnitude (or size) of an object's motion.

3. How do you find the average velocity?

The average velocity is calculated by dividing the total displacement (change in position) by the total time elapsed. The formula is: average velocity = (final position - initial position) / time.

4. What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity and can be calculated by dividing the change in velocity by the change in time. The units for acceleration are usually meters per second squared (m/s^2).

5. How do you solve for acceleration?

To solve for acceleration, you can use the formula: acceleration = (final velocity - initial velocity) / time. This means that the change in velocity divided by the change in time will give you the acceleration of an object.

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