If f(t)=−t2+5t+3 describes the distance that a ball has travelled in meters, what is the instantaneous rate of change of the ball at one second?

Jack and Jill ran up the hill at 2.9 m/s. The horizontal component of Jill's velocity vector was 2.5 m/s a. What was the angle of the hill? b.

Speedometer readings for a vehicle (in motion) at 12-second intervals are given in the table. t (sec) v (ft/s) distance traveled ~ 0 12 24 36 48 60 Estimate the distance traveled by the vehicle during this 60-second period using the velocities at the beginning of the time intervals. distance traveled feet 40 29 36 40 34 30 Give another estimate using the velocities at the end of the time periods. feet

An object's position as a function of time in one dimension is given by the expression; 3.8t2 + 2.3t + 8.15 where are constants have proper SI Units. What is the object's position at t = 2.57?

If an average-size man jumps from an airplane with an open parachute, his downward velocity t seconds into the fall is v(t) = 20(10.2) feet per second. (a) Use functional notation to express the velocity 3 seconds into the fall. Calculate it. ft per sec (b) Explain how the velocity increases with time. Include in your explanation the average rate of change from the beginning of the fall to the end of the first second and the average rate of " change from the fourth second to the fifth second of the fall. This answer has not been graded yet. (c)-Find the terminal velocity. ft per sec (d) Compare the time it takes to reach 99% of terminal velocity here with the 25 seconds it took a skydiver with his parachute closed to reach 99% of terminal velocity in Example 2.1. On the basis of the information we have, which would you expect to reach 99% of terminal velocity first, O feather feather or a cannonball? O cannonball Need Help? Read It

An engineer is testing how quickly a car accelerates from rest. The velocity V is measured in miles per hour, as a function of time t, in seconds, since the car is at rest. See the table below. What is the slope for the linear function modeling velocity as a function of time, V=,  and what would the formula be for the velocity at time 0, V(0) Time (t) Velocity (V) 2.0 28.9 2.5 35.0 3.0 41.1 3.5 47.2

Suppose your hair grows at the rate of 1/34 inch per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1 nm, your answer suggests how rapidly atoms are assembled in this protein synthesis.

The acceleration of an object (in m/s) is given by the function a(t) = 7 sin(t). The initial velocity of the object is v(0) 2 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = b) Find the object's displacement (in meters) from time 0 to time 3. meters c) Find the total distance traveled by the object from time 0 to time 3. meters

The velocity of a toy car moving along as straight path is shown in the figure. Match the numbers according to the graph. Assume the numbers in the choices are followed by proper units (not shown), i.e., distance in [m], speed or velocity in [m/s], and acceleration in [m/s^2].

High-speed motion pictures (3500 frames/second) of a jumping 230 μg flea yielded the data to plot the flea's acceleration as a function of time as shown in the figure ( Figure 1). (See "The Flying Leap of the Flea," by M. Rothschild et al. in the November 1973 Scientific American.) This flea was about 2 mm long and jumped at a nearly vertical takeoff angle. Use the measurements shown on the graph to answer the questions. Figure alg 150 100 50 0 0 0.5 1.0 1.5 Part E Use the graph to find the flea's maximum speed. Express your answer in meters per second to two significant figures. IVE] ΑΣΦ 3 v=1.6 Submit Previous Answers Request Answer ? X Incorrect; Try Again; 2 attempts remaining m/s