Question

A force of 5 N changes the velocity of a body from 36 km/h to 72 km/h in 5 s. How much force is needed to produce the same change in 2 s ? 1.25 N 12.5 N 125 N 0.125 N

Answer 1

Force needed to change body momentum = 5 N

Change in velocity (δ P) v2 - v1 = 36 km/ h or 10 m/s

Time taken = 5 sec

F = δ P / t

5 = m δv / t

5 = m × 10 / 5

m = 2.5

Hence force needed to produce same change in 2 sec

F = 2.5 × 10 / 2

F = 12.5 N

Answer 2

Hey Pretty Stranger!

• Initial Velocity (u) = 36 km/hr = 36 × $\sf\dfrac{5}{18}$ = 10 m/s

• Final Velocity (v) = 72 km/hr = 72 × $\sf\dfrac{5}{18}$ = 20 m/s

• Time (t) = 5 seconds

• Force (F) = 5 Newtons

We hafta find acceleration first

$\bigstar \: { \boxed{ \sf \: Acceleration = \frac{Final \: Velocity - Initial \: Velocity}{Time \: taken} }}$

$\longrightarrow \sf \: \dfrac{20 - 10}{5}$

$\longrightarrow \sf \: \dfrac{10}{5} = 2 \: m {s}^{ - 2}$

From Newton's 2nd Law of motion :

$\bigstar \: { \boxed{ \sf \: Force = Mass \times Acceleration }}$

$\longrightarrow \sf \: 5 = Mass \times 2$

$\longrightarrow \sf \:Mass = 2.5 \: kg$

Now, To bring the same change in 2 seconds :

$\bigstar \: { \boxed{ \sf \: Acceleration = \frac{Final \: Velocity - Initial \: Velocity}{Time \: taken} }}$

$\longrightarrow \sf \: \dfrac{20 - 10}{2}$

$\longrightarrow \sf \: \dfrac{10}{2} = 5m {s}^{ - 2}$

And now,

$\bigstar \: { \boxed{ \sf \: Force = Mass \times Acceleration }}$

$\longrightarrow \sf \: F = 2.5 \times 5$

$\longrightarrow \sf \: F =12. 5 \: N$

$\therefore$ 12.5 N of force is needed to produce the same change in 2 s.