Q. A car starts from point xi=0 and moving forward with a velocity of 15 m/s having an acceleration of 2 m/s^2 . It has to go till xf = 100m . Meanwhile a dog is running back and forth starting (from car to xf and from xf to car) with a speed of 10 m/s. Calculate how much distance dog has travelled when car reaches its final destination xf.
Answers
Given :-
◉ A car starts from point xᵢ = 0 m to xₙ = 100 m with initial velocity, u = 15 m/s moves forward having an acceleration, a = 2 m/s².
◉ In between, A dog is running back and forth starting with a speed, = 10 m/s
To Find :-
◉ Distance travelled by dog when car reached its final destination xₙ .
Solution :-
Let us find the time to be taken by the car to travel to xₙ.
Here, u = 15 m/s , and displacement, s = 100 m
acceleration, a = 2 m/s²
Using the second equation of motion,
⇒ s = ut + 1/2 at²
⇒ 100 = 15t + t²
⇒ t² + 15t - 100 = 0
⇒ t² + 20t - 5t - 100 = 0
⇒ t(t + 20) - 5(t + 20) = 0
⇒ (t + 20)(t - 5) = 0
So,
⇒ t = 5, -20
But we know, Time can't be negative
∴ Time taken, t = 5 s
Now, Let us find the distance travelled by dog in this interval.
⇒ Distance = Speed × Time
⇒ Distance = 10 × 5
⇒ Distance = 50 m
Hence, Distance travelled by dog is 50 m.