A car is travelling at 20 m/s when the driver sees a fallen tree 50 m ahead.
The driver's reaction time is 0.70 s. When the brakes are applied, the car decelerates uniformly at 6.25 m/s².
(a) Calculate the thinking distance. [2]
(b) Determine whether the car stops before it reaches the tree. [4]
- (a) distance = speed × time or $20 \times 0.70$(1)
- (a) 14 m(1)
- (b) $v^2 = u^2 + 2as$ with values, e.g. $0 = 20^2 - 2 \times 6.25 \times s$ or $20^2 = 2 \times 6.25 \times s$(1)
- (b) braking distance = 32 m(1)
- (b) stopping distance = 14 + 32 = 46 m allow ecf from (a)(1)
- (b) 46 m is less than 50 m so the car stops (4 m) before the tree conclusion must be consistent with candidate's total(1)
- Answer: (a) 14 m (b) stopping distance 46 m < 50 m, so it stops in time
- Examiner tip: Stopping distance = thinking distance + braking distance; using only the braking distance loses the comparison mark.