Question

Practice Problem • In 2.5 s a car increases its speed from 60 km/h to 65 km/h while a bicycle goes from rest to 5 km/h.
•Which undergoes the greater acceleration?
• What is the acceleration of each vehicle?

Answer 1

Answer:

they have same acceleration 2m/s^2

Explanation:

a =v-u/t

65-60/2.5

2m/s^2

Answer 2

a) The acceleration of the car and the bicycle are equal since $\delta V$ for both vehicle is 5km/h and the time taken for both vehicle is also the same 2.5s.

b) The acceleration of the bicycle is 0.556m/s²

Given the data in the question;

• Time taken for both car and bicycle; $t = 2.5s$

• Initial velocity of car; $u_c = 60km/h = 16.667m/s$

• Final velocity of car; $v_c = 65km/h = 18.0556m/s$

Since the bicycle starts from rest

• Initial velocity of the bicycle; $u_b = 0$

• Final velocity of the bicycle; $v_b = 5km/h = 1.38889m/s$

a)

The acceleration of the car and the bicycle are equal since $\delta V$ for both vehicle is 5km/h time taken for both vehicle is also the same 2.5s.

b)

The acceleration of each vehicle

To determine the acceleration for car and the bicycle, we use the first equation of motion:

$v = u + at$

Where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time.

Now, For the car;

$18.0556m/s = 16.667m/s + ( a + 2.5s )\\\\a = \frac{18.0556m/s - 16.667m/s }{2.5} \\\\a = \frac{1.3886m/s}{2.5s} \\\\a = 0.556 m/s^2$

Hence, the acceleration of the car is 0.556m/s²

For the bicycle;

$1.38889m/s = 0 + ( a * 2.5s )\\\\a = \frac{1.38889m/s}{2.5s}\\\\a = 0.556m/s$

Hence, the acceleration of the bicycle is 0.556m/s²

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