Question

Kinematics Problem:

A car accelerated from 6.3 mph to some final velocity over 2.1 s. Then, for the next 28.8 s the car was driving at this final velocity. The total distance traveled by the car over the entire time turned out to be 447.5 m.

What was acceleration of the car over the first 2.1 s?

Answer 1

Let u be the initial velocity in m/s

So,
u = m/s =

Now, let us take final velocity =v . it is given that the car accelerated and reached v m/s over 2.1 s.

Let's get the relation between final velocity(v) and initial velocity(u)

[ a is acceleration of the car]

-------------(1)

Now, distance travelled in this 2.1 second can be calculated by:

[ Here s is the distance travelled in 2.1 seconds ]

So,

---- (2)

Now, for next 28.8 second car is moving with final velocity (v)
So,

distance travelled during this time (s') = [ Putting the value of v from equation 1]

  

  

Now, given total distance travelled = 447.5 m

Also,
Total distance travelled =

On solving, we get

Hence,the acceleration of the car over the first 2.1 s is