Question

Force is applied to a body of mass $2\text{ kg}$ at rest on a frictionless horizontal surface as shown in the force against time ($F-t$) graph. The speed of the body after 1 second is

• A. $7.5\text{ m/s}$
• B. $12.5\text{ m/s}$
• C. $10\text{ m/s}$
• D. $15\text{ m/s}$

Hint:

Always remember that $\text{Impulse} = \text{Area}$. Finding the area under an $F-t$ curve gives you the change in momentum directly. Dividing that area value by the mass of the body gives the change in velocity instantly!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
A 2 kg body starting from rest is subjected to a force-time graph; find its final speed at t=1s using impulse.

Step 2: Key Formula or Approach:
Impulse (area under F-t graph) = change in momentum = m(v – u). With u=0, v = Impulse/m.

Step 3: Detailed Explanation:
Impulse = Area₁(0–0.5s: 10N) + Area₂(0.5–1s: 20N) = 0.5×10 + 0.5×20 = 5 + 10 = 15 N·s. v = 15/2 = 7.5 m/s.

Step 4: Final Answer:
Final speed is 7.5 m/s, matching option (A).