2. 1D Motion / Kinematics

The brakes of your car can provide an acceleration of 4.6m/s². You're speeding at 37.5 m/s and suddenly see a police car, so you slam the brakes. How long will it take for your car to slow down to the speed limit of 25 m/s?

Starting from rest, a car accelerated to 20⁢m/s in 4⁢s. What was the magnitude of the car's constant acceleration?

190

An explorer on the moon, where there is no atmosphere, simultaneously drops a hammer, a feather and a steel ball from the same height. Which will hit the ground first?

185

Hank the hammerhead shark was swimming in the negative direction with a speed of

2.0 m / s

. 1.0 second later he was swimming with a velocity of

- 4 m / s

. What was his average acceleration during the 1.0 second interval?

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of 20 m/s(45 mi/h) when it reaches the end of the 120-m-long ramp. (b) How much time does it take the car to travel the length of the ramp?

440

952

A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = (2.80 m/s3)t, where the +y-direction is upward. (b) What is the speed of the rocket when it is 325 m above the surface of the earth?

196

A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = (2.80 m/s3)t, where the +y-direction is upward. (a) What is the height of the rocket above the surface of the earth at t = 10.0 s?

989

rank

A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t) = 50.0 cm + (2.00 cm/s)t − (0.0625 cm/s^2)t^2. (a) Find the turtle's initial velocity, initial position, and initial acceleration.

698

CALC. A car's velocity as a function of time is given by v_x(t) = α + βt^2, where α = 3.00 m/s and β = 0.100 m/s^3. (a) Calculate the average acceleration for the time interval t = 0 to t = 5.00 s.

1214

rank

A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car's motion, the eastward component of the car's velocity is given by vx(t) = (0.860 m/s^3)t^2. What is the acceleration of the car when vx = 12.0 m/s?

1594

rank

A particle's velocity is given by the function 𝓋ₓ = (2.0 m/s) sin (πt), where t is in s. b. What is the particle's acceleration at that time?

116

A particle's velocity is described by the function vₓ = (t² ─ 7t + 10) m/s, where t is in s. b. What is the particle's acceleration at each of the turning points?

176

A good model for the acceleration of a car trying to reach top speed in the least amount of time is a𝓍 = a₀ ─ kv𝓍, where a₀ is the initial acceleration and k is a constant. b. Find an expression for the car's velocity as a function of time.

244

At this instant, the particle is speeding up and curving upward. What is the direction of its acceleration?

124

A sports car moving at constant velocity travels 120 m in 5.0 s. If it then brakes and comes to a stop in 3.7 s, what is the magnitude of its acceleration (assumed constant) in m/s², and in g's (g = 9.80 m/s²) ?

127

The position of an object is given by 𝓍 = At + Bt², where 𝓍 is in meters and t is in seconds.

(b) What is the acceleration as a function of time?"