Question

A sports car accelerates uniformly from rest to a speed of 87 mi/hr in 8s. Determine: a.The acceleration of the car

b.The distance the car travels in the first 8 s
c.The velocity of the car after the first 10 s

Answer 1

Part a)

`a = 4.86 m/s^2`

Part b)

`d = 155.52 m`

Part c)

`v_f = 48.6 m/s`

Step-by-step explanation:

As we know that car start from rest and reach to final speed of 87 mph

so we have

`v_f = 87 mph = 38.88 m/s`

now we have

Part a)

acceleration is rate of change in velocity

`a = (v_f - v_i)/(t)`

`a = (38.88 - 0)/(8)`

`a = 4.86 m/s^2`

Part b)

distance moved by car with uniform acceleration is given as

`d = (v_f + v_i)/(2) t`

`d = (38.88 + 0)/(2) 8`

`d = 155.52 m`

Part c)

As we know that the car start from rest

so final speed after t = 10 s

`v_f = v_i + at`

`v_f = 0 + (4.86)10`

`v_f = 48.6 m/s`