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1. (a) A frictionless car of mass 1.5 tonnes travels uphill along a slope at 20º to the horizontal for 0.5 km at 20 km per hour.

(i) How much work does the engine do on the car?
(ii) What power does the engine supply?

(b) The car the rolls back down the hill with the engine turned off. How fast is it travelling when it has rolled back to its starting position?

(c) The car continues to roll a further 0.5 km down the slope until it hits a solid wall, whereupon it is brought to rest in a distance of 20 cm as the front of the car crumples.

(i) What impulse is applied to the wall?
(ii) Assuming uniform deceleration, what is the average braking force applied to the car by the wall?

(d) If the driver had noticed the wall when the car had rolled back as far as the starting point and had applied the brakes at that point, what average braking force and power would have been required to stop the car just as it reached the wall?

2. A car travels northeastwards for 2.5 km, accelerating with constant acceleration from stationary to 80 km per hour over the first 0.4 km and then travelling at constant velocity and finally breaking with constant deceleration to 5 km per hour over the final 0.2 km, at which point it turns 65º to the south. It then travels for another 3.7 km, initially accelerating to 65 km per hour for 0.28 km and then travelling at constant velocity before finally coming to rest by braking with constant deceleration for 10 s.

(a) Represent this journey accurately on distance-time, speed-time and acceleration-time graphs.

(b) Calculate the total distance and final displacement, the time taken for the journey, the average speed and the average velocity.

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