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Question

# A particle moves along a straight line and its velocity depends on time t as v=4tâˆ’t2. Here v is in m/sec and t is in seconds. Then for the first 5 seconds:

A
Magnitude of average velocity is 53m/s
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B
Average speed is 135m/s
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C
Average speed is 115m/s
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D
Average acceleration is 1m/s2
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Solution

## The correct options are A Magnitude of average velocity is 53m/s B Average acceleration is −1m/s2 C Average speed is 135m/sAverage velocity =sΔt=vavgS=∫50vdt=∫50(4t−t2)dt=253mvavg=25/3m5sec=53msecAverage speed =distance coveredtime taken=distanceΔtDistance =∫40vdt+∫54(−v)dt=323+73=393m=13mAverage speed =13m5secAverage acceleration (aavg)=vf−viΔtvf=4×5−52=20−25=−5vi=0aavg=−5−05=−1m/s2

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