Question

Solve the following examples.

a) An object moves 18 m in the first 3 s, 22 m in the next 3 s and 14 m in the last 3 s. What is its average speed?

b) An object of mass 16 kg is moving with an acceleration of 3 m/s² . Calculate the applied force. If the same force is applied on an object of mass 24 kg, how much will be the acceleration?

c) A bullet having a mass of 10 g and moving with a speed of 1.5 m/s, penetrates a thick wooden plank of mass 90 g. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity.

d) A person swims 100 m in the first 40 s, 80 m in the next 40 s and 45 m in the last 20 s. What is the average speed?

Answer 1

a.
$$\begin{gathered} \text{Average speed=}\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Total}\mathrm{time}}=\frac{18+22+14}{3+3+3} \\ =\frac{54}{9}=\text{6 m/s} \end{gathered}$$

b.
(i) m = 16 kg, a = 3 m/s²
F = m $\times$ a
F = 16 $\times$ 3 = 48 N
Now, F = 48 N, m =24 kg
F = m $\times$ a
48 = 24 $\times$ a
a = 2 m/s²

c. Given,
Mass of bullet, m₁ = 10 g
Initial speed of bullet, u₁ = 1.5 m/s
Mass of plank, m₂ = 90 g
Initial speed of plank, u₂ = 0
From law of conservation of momentum,
m₁u_{1 +} m₂u₂ = m₁v₁ + m₂v₂
Since, the bullet gets embedded in the palnk and both move with the same speed, so v₁ = v₂ = v
So, we can rewrite the equation as
m₁u_{1 +} m₂u₂ = (m₁ + m₂)v
10 $\times$1.5 + 90 $\times$ 0 = (10 + 90)v
15 = 100v
$\Rightarrow$v = 0.15 m/s

d.
$$\begin{gathered} \text{Average speed =}\frac{\mathrm{Average}\mathrm{distance}}{\mathrm{Average}\mathrm{time}} \\ =\frac{100+80+45}{40+40+20}=\frac{225}{100}=2.25\text{m/s} \end{gathered}$$