3A car travelling at initial velocity 30m/s overtake a bus which was 120m ahead. The bus then moves with initial velocity 10m/s and accelerate at
5ms-2.
when will the bus also now overtake the car,

what is the time interval
between the arrival of the two cars if the car is to travel a total distance of
450m .

The bus is 120 m ahead of the car, so the car covers this distance in

120 m = (30 m/s) t

t = (120 m) / (30 m/s)

t = 4 s

Now take the car's position at the moment the car overtakes the bus to be the origin.

Car's position at time t :

x = (30 m/s) t

Bus's position at time t :

x = (10 m/s) t + 1/2 (5 m/s²) t²

The bus overtakes the car when their positions are equal:

(30 m/s) t = (10 m/s) t + 1/2 (5 m/s²) t²

t / (2 s) ((5 m/s) t - 40 m) = 0

t = 0  or  t = (40 m) / (5 m/s) = 8 s

If the car travels a total distance of 450 m, then it does so after

450 m = (30 m/s) t

t = (450 m) / (30 m/s)

t = 15 s

The bus overtakes the car in the first 12 s of this journey, so both vehicles reach the same destination with 3 s between them.

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