Question

An object is thrown straight upward. The velocity of the object 1 second after being thrown is 88 feet per second. The velocity of the object 3 seconds after being thrown is 24 feet per second. Write an equation that models the velocity of the object v, in feet per second at a time t seconds after being thrown? Assume that the velocity changes at a constant rate. A) v(t) = 88 - 32t B) v(t) = 88 + 32t C) v(t) = 88t - 32 D) v(t) = 88t + 32

Answer 1

The equation that models the velocity of the object is v(t) = 88 - 32t.

Step-by-step explanation:

The equation that models the velocity of the object at a time t seconds after being thrown is:

v(t) = 88 - 32t

The equation is derived from the fact that the velocity changes at a constant rate. The constant rate of change can be determined by finding the difference in velocity between two points in time. In this case, the velocity decreased by 64 feet per second over a time interval of 2 seconds (from 88 feet per second to 24 feet per second). Using this rate of change, we can determine the equation for the velocity of the object at any time t seconds after being thrown.

Answer 2

The correct equation that models the velocity of the object at a time t seconds after being thrown, based on the change in velocity due to gravity, is v(t) = 88 - 32t, which matches option A.

Step-by-step explanation:

The object thrown straight upward changes velocity at a constant rate due to gravity. The given velocities at different times can be used to calculate this rate of change, which is the acceleration. Since the change in velocity is from 88 feet per second to 24 feet per second over a 2-second interval, we can find the acceleration (which will be negative due to gravity) by the formula:

Acceleration = (Final velocity - Initial velocity) / Time interval

Acceleration = (24 ft/s - 88 ft/s) / (3 s - 1 s) = -64 ft/s² / 2 s = -32 ft/s².

Now we can write the equation for velocity as a function of time, starting at the initial velocity of 88 ft/s and changing by the acceleration multiplied by time:

v(t) = 88 - 32t

This corresponds to option A. Thus, the equation that models the velocity of the object v, in feet per second at a time t seconds after being thrown is v(t) = 88 - 32t.