Question

unit 1: 1.4f - 1 give number answers only. round answers to two decimal places. 1 formula 1 point an object starts 9.81 m from the origin at 7.45 m/s. it accelerates at 5.84 m/s/s for 2.64 sec. how far has it traveled? answer

Explanation:

Step1: Recall the kinematic equation for displacement with constant acceleration.

The formula for displacement \( s \) when an object has an initial velocity \( u \), acceleration \( a \), and time \( t \) is \( s = ut+\frac{1}{2}at^{2} \). Here, \( u = 7.45\space m/s \), \( a = 5.84\space m/s^{2} \), and \( t = 2.64\space s \).

Step2: Calculate the first term \( ut \).

Substitute the values of \( u \) and \( t \) into \( ut \): \( ut=7.45\times2.64 \).
\( 7.45\times2.64 = 19.668 \).

Step3: Calculate the second term \( \frac{1}{2}at^{2} \).

First, calculate \( t^{2} \): \( t^{2}=(2.64)^{2}=6.9696 \).
Then, calculate \( at^{2} \): \( at^{2}=5.84\times6.9696 = 40.702464 \).
Then, calculate \( \frac{1}{2}at^{2} \): \( \frac{1}{2}\times40.702464 = 20.351232 \).

Step4: Calculate the total displacement \( s \).

Add the two terms together: \( s=19.668 + 20.351232 \).
\( s = 40.019232 \).

Step5: Round to two decimal places.

Rounding \( 40.019232 \) to two decimal places gives \( 40.02 \).

Answer:

\( 40.02 \)