SPH 4U1

Graphing and 2 Body Motion (Catch Up Problems)

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1.      A cyclist starts from rest and accelerates uniformly for 16 s at 0.75 m/s2 [W]. She then cycles at a constant velocity for 55s, then slows to a stop with an acceleration of 0.60 m/s2 [E].

a) Find the total displacement of the cyclist from her starting point.

b) Find the average velocity of the cyclist.

2.    An object starts from rest, accelerates at 4.0 m/s2 [W], and then suddenly accelerates at 8.0 m/s2 [E] finally coming to a stop. The displacement is 1.2 x 103 m [W]. Find:

a) The total time taken.

b) The maximum velocity of the object.

3.    Car A is traveling at 11 m/s [N] when it passes a stationary Car B. When Car A is 20. m ahead of Car B, B begins to accelerate at a uniform  rate of 4.0 m/s2 [N] and at that instant, Car A begins to accelerate at a uniform rate of 2.0 m/s2 [S].

a) Determine when B catches up with A.

b) Determine how far B has gone when it has caught up with A.

4.     A sports car is travelling along a highway at a constant velocity of 36 m/s [N] exceeding the speed limit. It passes an unmarked police car parked on the shoulder of the highway. The police car accelerates from rest, 3.0 s after the sports car passed it, at the rate of 6.0 m/s2 [N] until it reaches a velocity of 48 m/s [N]. It maintains this velocity until it catches up to the sports car.

a) Find the time it takes the police car to catch up to the sports car, starting from the time when the sports car went past.

b) The distance travelled by the police car while catching up to the sports car.

5.    A truck with one headlight is travelling at a constant speed of 18 m/s when it passes a stopped police car. The police car sets off in pursuit at a constant acceleration of magnitude 2.2 m/s2.

a) How far does the cruiser travel before catching the truck?

b) How long does the pursuit last?

6.     The driver of a pink Cadillac travelling at a constant 26.8 m/s is being chased by a police car. The police car is 20. m behind the Cadillac when it too reaches 26.8 m/s, and at that moment the police floors the gas pedal. If the police roars up to the rear of the Cadillac 2.0 s later what was the scalar value of the police's acceleration, assuming it to be constant. [hint: this problem really begins when the police gets to a point 20 m behind the Cadillac. At that moment the two cars are at reast with respect to each other. The police then takes another 2.0 s to cover the 20.m distance].

7.     Superman is jogging alongside the railroad tracks on the outskirts of metropolis at 100. km/h. He overtakes the caboose of a 500. m long freight train travelling at 50. km/h. At that moment he begins to accelerate at 10 m/s2. How far will the train have travelled before Superman passes the train?

1.     a) 8.8x102m [W]          b) 9.6 m/s [W]

2.     a) 3.1x101s                  b)  8.0x101m/s [W]

3.     a) 5.0 s                        b) 50. m

4.    a)  2.5x101s                  b) 1.0 km

5.    a)  2.9x102m                b) 16 s

6. 10. m/s2.

7. 0.12 km