# Solving for Distance, Velocity and Acceleration

• jenny121
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.
jenny121
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

PhDeezNutz and anuttarasammyak
Your calculus looks fine. You might question the dimensional aspects of these equations, which the problem setter has chosen to ignore.

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.

PeroK
I see, thanks. after putting the unit it makes more sense now

berkeman

## 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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