A car starts moving along a line, first with acceleration a=5 `ms^(-2)` starting from rest then uniformly and finally decelerating at the same rate a, comes to rest.The total time of motion is `tau=25 s`. The average velocity during the time is equal to lt v gt =72 km/hr.How long does the partial move uniformly ?

Options

A. 10 s
B. 12 s
C. 20 s
D. 15 s

Answer

D

Explanation

Average velocity `=("Total displacement")/("Total time")`

or `20=((1)/(2)xxaxxt^(2)+(at)(25-2t)+(1)/(2)xxaxxt^(2))/(25)`
Solving this equation with `a = 5ms^(-2)` we get, t = 5 s
Thus, the particle moved uniformly for `(25-2t)` or 15s.