Question

a car in a drag race started from rest and accelerated constantly to a velocity of 50 m/s when it reached the end of a 500 m road. What was the cars rate of acceleration?

Answer 1

The acceleration of the car is
`2.5(m)/(s^(2) )`

Step-by-step explanation:

Kinematics of the problem:

The car moves with uniform accelerated movement, then, We use the acceleration equation for this type of movement:

`a=(1)/(2*d) (v_(f) ^(2) -v_(i) ^(2) )` Formula 1

vf: final speed=
`50(m)/(s)`

vi: initial speed=0

d=distance traveled by the car=500m

Acceleration calculating:

We replace known information in the equation 1:

`a=(50^(2) -0)/(2*500)`

`a=(2500)/(1000)`

`a=2.5(m)/(s^(2) )`

Answer:

The acceleration of the car is
`2.5(m)/(s^(2) )`

Answer 2

Use the kinematic equation,
`v _(f) ^(2) = v _(o) ^(2) + 2a ( x_(f) - x_(o) )`
use your givens, v initial is 50m/s, v final would be 0m/s since the car is coming to a rest, x final would be 500m, x intial would be 0m, and you are looking for your acceleration. plug in your givens into your equation:

`(50) ^(2) = (0) ^(2) + 2(a)(500)`

so, by solving for a, you would get 2.5m/s
`^(2)`