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On earth, A falling object has a downward acceleration of 32 feet per second per second due to gravity. Suppose an object falls from an initial height of s0,With an initial velocity of v0feet per second, Use antiderivatives to show that the equations for the position and velocity of the object after t seconds are respectively s(t)=-16t2+v0t+s0andv(t)=-32t+vo(t)

Short Answer

Expert verified

We use antiderivatives to show that the equations for the position and velocity of the object after t seconds are respectively s(t)=-16t2+v0t+s0andv(t)=-32t+v0

Step by step solution

01

Given information

The downward acceleration of a falling object is 32 feet

02

use antiderivatives to find the equations of v0,s0

As the downward acceleration of the falling object is 32 feet per second second

We get,

a(t)=-32

Now when we derivate the velocity function we get acceleration

We use targeted guess nd check method

Since on differentiating the power function decreases its power by one Hence we start by function

v(t)=t+v0as at t=0 we the velocity becomes initial velocity

The equation is nearly equal now we just have to adjust the coefficients

We get,

v(t)=-32t+v0 (1)

03

Now we find equation of distance

Similarly,

We use targeted guess nd check method

Since on differentiating the power function decreases its power by one Hence we start by function

s(t)=t2+v0t+s0

Which is nearly equal now we adjust the coefficients

s(t)=-16t2+v0t+s0

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Most popular questions from this chapter

Use (a) the hโ†’0definition of the derivative and then

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Every morning Linda takes a thirty-minute jog in Central Park. Suppose her distance s in feet from the oak tree on the north side of the park tminutes after she begins her jog is given by the function s(t)shown that follows at the left, and suppose she jogs on a straight path leading into the park from the oak tree.

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(d) Approximate the times at which Lindaโ€™s (instantaneous) velocity was equal to zero. What is the physical significance of these times?

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