Calculate the power a car engine contributes to speeding the 1400 kg car up to a highway speed of 60.0 mi/h in 14.0 s.

35.6 kW

Explanation:

Given data

mass (m): 1400 kg

speed (v): 60.0 mi/h. In SI units,

time (t): 14.0 s

The acceleration (a) of the car is:

The force (F) exerted is:

F = m × a = 1400 kg × 1.91 m/s² = 2.67 × 10³ N

The distance (d) travelled is:

d = 1/2 × a × t² = 1/2 × 1.91 m/s² × (14.0 s)² = 187 m

The work (w) done is:

w = F × d = 2.67 × 10³ N × 187 m = 4.99 × 10⁵ J

The power (P) of the car engine is:

P = w / t = 4.99 × 10⁵ J / 14.0 s = 3.56 × 10⁴ W = 35.6 kW

The greatest speed of the car is 19.36m/s

Explanation:

The maximum speed the car will attain without skidding is given by:

F= uN = umg ...eq1

But F = mv^2/r

mv^2/r = umg

Dividing both sides by m, leaves you with:

V= Sqrt(ugr)

Where u = coefficient of static friction

g = acceleration due to gravity

r = raduis

Given:

U = 0.82

r=0.82

g= 9.8m/s

V = Sqrt(0.82 × 9.8 × 45)

V = Sqrt(374.85)

V = 19.36m/s