Answer to Question #717 in Mechanics | Relativity for Rooky

Question

If a car starts from rest and accelerates at 5.0 m/sec^2 for 6.0 seconds, how far did it travel and how fast was it moving at the end of the 6.0 seconds?



Can you show work please?

Answer 1

The motion of the car in that 6 seconds have been a motion with constant acceleration. One of the
equations of motion of a body in constant acceleration is:
a=Δv/Δt⇒Δv=a*Δt
⇒v-v0=a*Δt⇒v=a*Δt+v0
Where v is the final velocity and v0 is the initial velocity and v0 = 0. Now with all the data we have, we can get for the final velocity:
v=a*Δt=5*6=30m/s
For the distance the car traveled in that time, we use another one of the equations of motion of a body in constant acceleration, namely the time-independent one:
v²-v²0=2a*Δx⇒Δx=(v²-v²0)/2a
and since v0 = 0 we get Δx=v²/2a
and using the data we have, we get Δx=v²/2a=30²/2*5=900/10=90m
We could nd the distance by another method, using another equation of motion:
Delta;x=x-x0=1/2a*t²+v0*t=1/2*5*6²+0=90m