A particle moves along a straight line and its velocity depends on time as `v=6t-3t^(2)` where 'v' is in m/sec and 't' is in sec. Find average velocity and average speed for first four seconds.

Options

A. `2 m//sec`
B. `4 m//sec`
C. `6 m//sec`
D. `8 m//sec`

Answer

C

Explanation

Avg. speed `= ("total distance")/("time taken")`
`v = 3t (2 - t) gt 0`
`t (t - 2) lt 0`
`v gt 0` for `t = 0` to `t = 2s`
`v lt 0` for `t = 2s`, to `t = 4s`
distance `= underset(0)overset(2)int (6t - 3t^(2)) dt + underset(2)overset(4)int (3t^(2) - 6t)dt`