a biker starts a race and crosses the half line in 3 second with speed 54km/h and after that he increases his speed uniformally at a rate 7.5m/s² and completed the race in 5 second.choose the correct option - 1.Acceleration in the first half is 5 m/s².2.He finished the rae with speed 108km/h.3acceleration in the second half of the race is 12.5m/s².NOTE MORE THAN ONE OPTION CAN BE CORRECT
Answers
Given : A biker starts a race and crosses the half line in 3 second with speed 54 km/h and after that he increases his speed uniformly at a rate 7.5 m/s²and completed the race in 5 second
To Find : Correct option
(A) Acceleration in the first half of the race is 5 m/s2
(B) He finished the race with speed 108 km/h
(C) Acceleration in the second half of the race is 12.5 m/s2
Choose the correct option.
Solution:
Speed = 54 km/hr = 54 * 1000/3600 = 15 m/s
Time = 3 sec
Distance = 15 * 3 = 45 m
increases his speed uniformly at a rate 7.5 m/s2 and completed the
race in 5 second
u = 15 m/s
a = 7.5 m/s²
t = 2 sec
v = u + at
=> v = 15 + 7.5*2 = 30 m/s
30 * 3600 / 1000 = 108 km/hr
d = (1/2) (15 + 30) * 2 = 45 m
Acceleration in the first half of the race is 5 m/s2 INCORRECT
as acceleration is ZERO
He finished the race with speed 108 km/h - CORRECT
Acceleration in the second half of the race is 12.5 m/s² incorrect as its given 7.5 m/s²
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Explanation:
I hope it will help you
so for first half u=0 because it starts the race, final velocity is =54km/hr =15m/s
calculate acceleration for first half
Acc = V-U/t
Acceleration= 15-0/3
acceleration=5m/s²
THAT MEANS OUR OPTION ACCELERATION IN THE FIRST HALF OF RACE IS 5M/S² IS CORRECT
now calculate acceleration for second half
acceleration is given to you in question=7.5 and time is 5sec but final velocity you have to find. intialvelocity will be 15m/s.
now we know A=V-U /t
7.5m/s²=v-15/5-3(time for second half -time for 1 half)
solve it .... 30m/s = Velocity final
now use options check 30m/s in km/hr it will be 108km/hr and [option c acceleration for second half is 12.5 is wrong question has already provided acc for second is 7.5]
THE SPEED THROUGH WHICH HE FINISHED RACE IS 108 km/hr
OPTION 1) acceleration in first half of the race is 5m/s²
OPTION 2) he finished the race with speed 108km/hr
ARE CORRECT