Constant Acceleration

The graph shows position versus time for an object moving with constant acceleration. What is the acceleration represented by the graph if the starting velocity is 0 m/s? Let υ_0x = 0 m/s, x_0 = 0 m, x = 15 m, and t = 4 s.

1.88 m/s^2 x = x_0 + v_(0x)t + 1/2s_xt^2 15 m = 1/2 a (4s)^2 1.88 m/s^2 = a

A car stops at an intersection and waits until the traffic is clear. It then accelerates from rest at a constant rate of 3 m/s2. What is the velocity of the car after 4 s?

12 m/s

A person holding a checkered flag high in the air stands 4 m in front of a line of race cars. When the flag is dropped, the race begins. By the time the cars reach the flag, they are traveling at 1.7 m/s. From there they accelerate at a constant 5.6 m/s^2. Find their position 7 s after they pass the flag.

153 m x-4 = (1.7)(7) + 1/2 (5.6)(7)^2 = 153

A car enters the highway at 16 m/s and accelerates at a constant rate of 3 m/s^2. How far does the car travel in 6.2 s?

157 m

Suppose a car is traveling at 12 m/s and accelerates at a constant acceleration of 3.7 m/s2 in light traffic. How long does it take the car to reach 25 m/s?

3.5 s

A car initially traveling at 14 m/s accelerates at a constant 3.2 m/s2 as it merges onto a highway. What is the car's velocity when it reaches its cruising speed 5 seconds later?

30 m/s

A rollercoaster is moving at 8.2 m/s just at the top of its largest hill. Assuming it has a constant acceleration of 6.8 m/s2, what is its speed when it reaches the bottom of the hill 3.8 s later?

34 m/s

A cat drops from a shelf 4.0 ft above the floor and lands on all four feet. Gravity causes the cat to fall with a constant acceleration of -9.8 m/s^2 (assuming up to be the positive direction). His legs bring him to a stop in a distance of 12 cm. Calculate his speed when he first touches the floor. Remember that 1 m = 3.28 ft.

4.6 m/s v_x^2 = (0)^2 + 2(-g)(0.12m - 1.2 m) = 21.17 m^2/s^2 v_x = -4.6 m/s

A motorcycle is traveling east at a rate of 56 mph. It takes 6.7 s for it to decrease its speed to 35 mph. How far does the motorcycle travel in 6.7 s if it slows at a constant acceleration? Remember 1 mile equals 5280 ft.

447 ft east of the sign average velocity = (v_(0x) + v_x)/2 =(56+35)/2 =45.5 mph=66.7 ft/s (average velocity)(time) = (66.7)(6.7)=447

When a bullet is fired from a gun, it accelerates at 2.0 × 105 m/s^2 and reaches its maximum velocity in 0.003 seconds. What is the final velocity of the bullet at the end of that interval?

600 m/s

The fastest measured pitched baseball left the pitcher's hand at a speed of 45.0 m/s. If the pitcher was in contact with the ball over a distance of 1.50 m and produced constant acceleration, what acceleration did he give the ball?

675 m/s^2 a_x = ((45.0 m/s)^2(0 m/s)^2)/2(1.50 m-0m) = (2025 m^2/s^2)/3 m = 675 m/s^2

The moment a car merges onto the freeway it is traveling at 27 m/s. However, traffic is moving a bit faster so the car continues to accelerate at a rate of 4.2 m/s^2 for another 2.3 seconds. How far does the car travel during that time?

73 m (27)(2.3) + 1/2 (4.2)(2.3)^2 = 73

A motorcyclist traveling east passes a sign that says he is entering the city and the speed limit is 35 mph. After 8 miles, he passes another sign notifying him that he is leaving the city and the speed limit is 55 mph. It takes 5.2 s for him to increase his speed to 55 mph. How far from the first sign is the motorcyclist by the time he reaches 55 mph?

8.07 miles average velocity = 45 mph = 0.0125 mi/s (0.0125)(5.2s) = 0.065 mi 8 + 0.065 = 8.07

A bullet is fired from a gun and it accelerates at 2.0 × 10^5 m/s^2. It reaches its maximum velocity in 0.003 seconds. How far has the bullet traveled by the time it reaches its maximum velocity?

0.9 m x-x_0 = v_(0x)t + 1/2a_xt^2 =1/2 (2.0 x 10^5 m/s^2)(0.003 s)^2 =0.9 m