A car starts from rest and accelerates uniformly to 20 m s-1 in 5 seconds. Class 9

A car starts from rest and accelerates uniformly to 20 m s^-1 in 5 seconds. Class 9

Question 1.

A car starts from rest and accelerates uniformly to 20 m s^-1 in 5 seconds. It then travels at 20 m s^-1 for 10 seconds and finally applies the brake (with uniform acceleration) to stop in 6 seconds. Find the total distance travelled. Class 9

Answer:

The motion has three phases:

Phase 1: Acceleration from rest to 20 m s^-1 in 5 s

u = 0 m s^-1,

v = 20 m s^-1,

t = 5 s

s₁ = 1/2 (u + v) × t

= 1/2 × (0 + 20) × 5

= 1/2 × 20 × 5 = 50 m

(Or using s = ut + 1/2at²: a = 20/5 = 4 m s^-2, s = 0 + 1/2 × 4 × 25 = 50 m ✓)

Phase 2: Constant velocity at 20 m s^-1 for 10 s

u = v = 20 m s^-1,

t = 10 s

Distance s₂ = v × t

= 20 × 10 = 200 m

Phase 3: Braking from 20 m s^-1 to rest in 6 s

u = 20 m s^-1

v = 0 m s^-1,

t = 6 s

Distance s₃ = 1/2 (u + v) × t

= 1/2 × (20 + 0) × 6

= 1/2 × 20 × 6 = 60 m

Total distance travelled

= s₁ + s₂ + s₃

= 50 + 200 + 60 = 310 m