Question

A car of mass 940.0 kg accelerates away from an intersection on a horizontal road. When the car speed is 42.5 km/hr (11.8 m/s), the net power which the engine supplies is 4300.0 W (in addition to the extra power required to make up for air resistance and friction). Calculate the acceleration of the car at that time.

Answer 1

Answer: The acceleration of the car at that time is 0.39 m/s^2

Explanation:

Power (P) is given by

Power (P) = work done (W) / time (t)

But, work done (W) = force (F) × displacement (d)

Therefore,

Power (P) = (F × d) / t

But, velocity (V) is defined by

Velocity (V) = displacement (d) / time (t)

Hence,

Power (P) = Force (F) × Velocity (V)

P = F × V

Where P is power is Watts (W)

F is force is Newtons (N)

and V is velocity in meter / second (m/s)

To calculate the acceleration, we will first determine the Force, F

From the question,

P = 4300.0W

V = 11.8 m/s

Therefore,

4300.0 = F × 11.8

F = 4300.0 ÷ 11.8

F = 364.407N

From the formula,

F = m × a

Where m is the mass

a is the acceleration

and F is force

Acceleration is given by,

a = F / m

From the question,

m = 940.0 kg

Hence,

a = 364.407 / 940.0

a = 0.39 m/s^2

Answer 2

Answer:

0.39 $m/s^2$

Explanation:

Parameters given:

Mass of car, m = 940 kg

Speed of car, v = 11.8 m/s

Power supplied by engine, P = 4300 W

To get the acceleration, we must define the relationship between Power and velocity.

Power, P, is given in terms of velocity, v, as:

P = F * v

where F = force

This is because Power is given as:

$P = \frac{E}{t} \\\\\\P = \frac{F*d}{t} \\\\\\=> P = F * v$

(where E = energy. t = time taken, d = distance moved)

Force, F, is given as:

F = m*a

Therefore, Power will be:

P = m * a * v

Acceleration, a, will then be:

$a = \frac{P}{m*v}$

$a = \frac{4300}{940 * 118} \\\\\\a = 0.39 m/s^2$

The acceleration of the car at that time is 0.39 $m/s^2$