Question

A 1200 kg car starts from rest and travels 100m in a time of 10 seconds . A) what is the acceleration of the car? B) what force must have acted on the car during this time? C) what is the velocity of the car after 10 seconds? D) what work was done on the car? E) what minimum power did the engine produce?

Answer 1

Given:
Mass (m) = 1200 kg
Distance (s) = 100 m
Time (t) = 10 seconds
Now,

`velocity (v) = (distance)/(time)`

=
`(100~ m)/(10~seconds)`

= 10 m/s
Note that this one is the final velocity.
We also know that,
initial velocity (u) = 0 m/s ....... because the car starts from rest.
Now,

`acceleration (a)= (change~in~velocity)/(time)`

=
`(v-u)/(t)`

=
`(10-0)/(10)`

= 1 m/s²
Now,
Force (F) = mass (m) * acceleration (a)
= 1200 kg * 1 m/s²
= 1200 kg.m/s²
= 1200 N
Now,
Work Done (W) = Force (F) * displacement (s) ....note that displacement is same as distance.
= 1200 N * 100 m
= 120000 N.m
= 120000 J
Now,
Power (P) =
`(Work~done(W))/(time(t))`

=
`(120000~J)/(10s)`

= 12000 J/s
= 12000 watt
SO,
A) The acceleration of the car is 1 m/s².
B) 1200 Newton (N) force must have acted on the car.
C) The velocity of the car after 10 seconds is 10 m/s.
D) 120000 Joule (J) work was done on the car.
E) The engine produced a minimum power of 12000 watt.