Question

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.

Answer 1

Power is calculated by dividing the work done with the time interval of the motion. Work, on the other hand, is force times the distance traveled. Therefore, we can calculate as follows:

60.0 mi/h = 26.82 m/s

The car accelerates at: 

v2 = v1 + at 
a = [v2 - v1] / t 
a = 1.49m/s² 

The distance it travels at this acceleration in 15.0 s is: 

d = [v1 + v2] t / 2 
d = (0 + 22.4m/s)15.0s / 2 
d = 168m 


P = m (a)(d) / t 
= (1300kg) (1.49m/s²) (168m) / 15.0s 
= 22,700 W

Answer 2

Answer:

35.6 kW

Explanation:

Given data

mass (m): 1400 kg

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

$\frac{60.0mi}{h}.\frac{1609.34m}{1mi}.\frac{1h}{3600s} =26.8m/s$

time (t): 14.0 s

The acceleration (a) of the car is:

$a=\frac{\Delta v}{t} =\frac{26.8m/s}{14.0s} =1.91m/s^{2}$

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