A car starts from rest and accelerates uniformly to a maximum velocity of 20 m/s . It then maintains this constant velocity for the remainder of its journey. If the total time of the journey is 15 s and the total distance covered is 250 m , the time for which the car was accelerating is:

Step-by-step solution

Let the time for which the car accelerates be t₁ . The velocity-time graph of the car consists of a triangular region from t = 0 to t = t₁ (during acceleration) and a rectangular region from t = t₁ to t = 15 s (during constant velocity). The total distance covered is the area under the velocity-time graph. Area of the triangular part = 1 2 base height = 1 2 t₁ 20 = 10t₁ Area of the rectangular part = length width = (15 - t₁) 20 = 300 - 20t₁ Total distance = 10t₁ + 300 - 20t₁ = 300 - 10t₁ Given that the total distan