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Question

A particle moves along a straight line and its velocity depends on time as v=4tt2. Then for first 5 s

A
Average velocity is 253 m/s
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B
Average speed is 10 m/s
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C
Average speed is 135 m/s
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D
Acceleration is 4 m/s2 at t = 0
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Solution

The correct option is D Acceleration is 4 m/s2 at t = 0
According to question
v=4tt2
Displacement =dx=vdt
Average velocity v=Total displacementTotal time=50vdt50dt=50(4tt2)dt50dt
=[2t2t33]505=5012535=253×5=53 ms1
Let us put v=0, we get
4tt2=0
t=0 and t=4 s
After t=4 s, the direction of motion will get reversed
Average speed =∣ ∣40vdt∣ ∣+∣ ∣54vdt∣ ∣50dt
=∣ ∣40(4tt2)dt∣ ∣+∣ ∣54(4tt2)dt∣ ∣5
=[2t2t33]40+[2t2t33]545
=(32643)+2(2516)13(12564)5=135 ms1
For acceleration a=dvdt=ddt(4tt2)=42t
At t=0,a=4 m/s2
option c and d are correct.

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