Question

A car accelerates uniformly from rest to 16.4 m/s in 4.35 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is 9.11 x 103 N, and (b) the weight of the car is 1.98 x 104 N.

Answer 1

Answer:

(a) Average power required to accelerate is 2.87 x 10⁴ W

(b) Average power is required to accelerate is 6.25 x 10⁴ W

Explanation:

Given :

Initial speed of car, u = 0 m/s

Final speed of the car, v = 16.4 m/s

Time, t = 4.35

Initial kinetic energy of car, K₁ = 0

Final kinetic energy of car, K₂ = (mv²)/2

Here m is the mass of the car.

Applying Work-Energy theorem,

Work done = Change in kinetic energy

W = ΔK    ....(1)

Power is defined as work done per unit time. So,

P = W/t

From equation (1), the above equation becomes:

P = ΔK/t

P = (K₂ - K₁)/t

P = (mv²)/(2t)   .....(2)

(a) Weight of the car, W = 9.11 x 10³ N

But, W = m x g

Here g is acceleration due to gravity.

So, m = W/g

Thus, the equation (2) becomes:

$P=\frac{Wv^{2} }{2gt}$      ....(3)

Substitute the suitable values in the above equation.

$P=\frac{9.11\times10^{3}\times (16.4)^{2} }{2\times9.8\times4.35}$

P = 2.87 x 10⁴ W

(b) Weight of the car, W = 1.98 x 10⁴ N

Substitute this value of W in equation (3) with other suitable values.

$P=\frac{1.98\times10^{4}\times (16.4)^{2} }{2\times9.8\times4.35}$

P = 6.25 x 10⁴ W