Question

Activity: Solve each problem involving acceleration. Be sure to show all solutions and to use the correct units. 1. While traveling along a highway a driver slows from 45 m/s to 15 m/s in 12 seconds. What is the automobile's acceleration? 2. A biker accelerates at a rate of 7 m/s2. How long will it takes the biker to reach a speed of 18 m/s?

Answer 1

Answer:

1. a = - 2.5 m/s²

2. t = 2.57 s

Explanation:

1.

The acceleration of the driver can be found using the first equation of motion:

$v_f = v_i + at$

where,

vf = final speed = 15 m/s

vi = initial speed = 45 m/s

a = acceleration = ?

t = time = 12 s

Therefore,

$15\ m/s = 45\ m/s +a(12\ s)\\\\a = \frac{15\ m/s-45\ m/s}{12\ s}$

a = - 2.5 m/s²

negative sign indicates deceleration

2.

The time taken by the biker to accelerate can be found by using the first equation of motion again:

$v_f = v_i + at$

where,

vf = final speed = 18 m/s

vi = initial speed = 0 m/s

a = acceleration = 7 m/s²

t = time = ?

Therefore,

$18\ m/s = 0\ m/s +(7\ m/s^2)t\\\\t = \frac{18\ m/s}{7\ m/s^2}$

t = 2.57 s