JEE Main 2023 · 13 April · evening · Single correct · +4 / −1
The distance travelled by an object in time t is given by s=(2.5) t². The instantaneous speed of the object at t=5 s will be:
- (a) 5 ms⁻¹
- (b) 12.5 ms⁻¹
- (c) 62.5 ms⁻¹
- (d) 25 ms⁻¹
Answer and solution
Answer (d) 25 ms⁻¹
Solution
Physics sir · 3 steps
Instantaneous speed is the slope of distance with time, so differentiate s first and then put in t = 5 s.
- Differentiate. Instantaneous speed is v = ds/dt. Differentiating s = 2.5t² gives the following.
v = d/dt(2.5t²) = 2 × 2.5 t = 5t
- Put in t. At t = 5 s, v = 5 × 5 = 25 m s⁻¹.
- So. The instantaneous speed at t = 5 s is 25 m s⁻¹, option (d).
The idea to keep. Speed at an instant always means ds/dt evaluated at that instant. Dividing total distance by total time gives only the average speed.
Answer from the NTA final answer key. Solution by PrepWiser.