Question

Rohan start moving on his bike from rest. Mass of Rohan and his bike is 150 kg. He wants to cover the first 100 M distance in least time. If engine of his bike can produce a maximum accelerating force of 750 N and air drag is negligible then find the minimum time taken by Rohan to cover first 100 M.

Answer 1

Given data : Rohan start moving on his bike from rest. Mass of Rohan and his bike is 150 kg. He wants to cover the first 100 M distance in least time. If engine of his bike can produce a maximum accelerating force of 750 N and air drag is negligible.

To find : The minimum time taken by Rohan to cover first 100 M ?

Solution : According to given data,

• Mass of Rohan and his bike, m = 150 kg
• Accelerating force, F = 750 N
• Covering distance, s = 100 m

We need to find acceleration of Rohan and his bike.

Now,

⟹ Force = mass * acceleration

⟹ 750 = 150 * acceleration

⟹ acceleration = 750/150

⟹ acceleration = 5 m/s²

According to given data initial velocity ( u ), of Rohan and his bike is zero ( 0 ),

Now, to find time taken by Rohan to cover first 100 m we use kinematical equation,

⟹ s = ut + ½ at²

⟹ 100 = 0 * t + ½ * 5 * t²

⟹ 100 = 5/2 t²

⟹ 5 t² = 100 * 2

⟹ 5 t² = 200

⟹ t² = 200/5

⟹ t² = 40

⟹ t = √40

⟹ t = 2√10

⟹ t = 6.3245 sec

Answer : The minimum time taken by Rohan to cover first 100 m is 6.3245 sec.