A car starts from rest and accelerates uniformly for 10 s to a velocity of 8 m/s It then - Science - Motion

Question

A car starts from rest and accelerates uniformly for 10 s to a
velocity of 8 m/s It then runs at a constant velocity and is
finally brought to rest in 64 m with a constant retardation The
total distance covered by the car is 584 m Find the value of
acceleration, retardation and total time taken

Bapan Pathak · Accepted Answer

The
car starts from rest and accelerates uniformly for 10 s to a
velocity of 8 m/s The acceleration is found to be,
a = (v â€“ u)/t = (8
â€“ 0)/10 = 0 8
m/s2
Distance traveled during this time
is,
S
= 0 + Â½ at2
=> S = 0 5 X 0 8 X
102
=> S = 40 m
Suppose it travels 'x' distance with constant
velocity, 8 m/s, for time 't'
It
then travels 64 m with uniform retardation and comes to
rest
Total distance traveled = 40+x+64 =
584
=> x = 480 m
So, 8 X t = 480
=> t = 60 s
Let the car travel 64 m with uniform
retardation for time t/
Using,
v2 = u2 - 2aS
=> 0 = 82 - 2(a)(64)
=> a = 0 5 m/s2
Retardation = 0 5 m/s2
t/ = (8)/(0 5) = 16 s
Total time taken is
= 10 s + 60 s + 16 s =
86 s

A car starts from rest and accelerates uniformly for 10 s to a velocity of 8 m/s. It then runs at a constant velocity and is finally brought to rest in 64 m with a constant retardation. The total distance covered by the car is 584 m. Find the value of acceleration, retardation and total time taken.