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.

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?

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. (a) What is the acceleration of the car?

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?

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?

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.

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?

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?

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?