Q.
A particle moves along a straight line and its velocity depends on time as v = 4t - t2. Then for first 5 s:
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a
Average velocity is 25/3 ms-1
b
Average speed is 10 ms-1
c
Average velocity is 5/3 m s-1
d
Acceleration is 4 ms-2 at t = 0
answer is C.
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Detailed Solution
Average velocity,v=∫05 vdt∫05 dt=∫05 4t−t2dt∫05 dt=2t2−t33055=50−12535=253×5=53 ms-1For average speed, let us put v = 0, which gives t = 0 and t = 4 s∴ Average speed =∫04 vdt+∫45 vdt∫05 dt=∫04 4t−t2dt+∫45 vdt5 =2t2−t3304+2t2−t33455 =2t2−t3304+2t2−t33455=135ms−1 For acceleration: a=dvdt=ddt4t−t2=4−2t At t=0, a=4 ms−2Therefore, options (3) and (4) are correct, and options (1) and (2) are wrong.
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