If an object with uniform acceleration (or deceleration) has a speed of #5 m/s# at #t=0# and moves a total of 125 m by #t=8#, what was the object's rate of acceleration?

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Answer 1 · 2016-01-28T05:03:11

The acceleration is #"1 m/s"^2"#.

We will use the following equation to determine acceleration.

#color(red)(a=(v_f-v_i)/(Delta t))#,

where #a="acceleration"#, #v_f="final velocity"#, #v_i="initial velocity"#, and #Delta t="time interval"#.

However, we must first determine the final velocity using the following equation.

#color(blue)(v_f=(Deltad)/(Delta t))#,

where #Delta d="change in position"#, and #Delta t="time interval"#.

#v_f=(125"m")/(8"s")#

#v_f="15.625 m/s"#

Now that we have the final velocity, we can use the first equation to determine the acceleration.

#color(red)(a=(v_f-v_i)/(Delta t))#

#color(red)(a=((15.625"m/s")-(5"m/s"))/(8"s"))#

#color(red)(a=(10.625"m/s")/(8"s"))#

#color(red)(a="1 m/s"^2")# (rounded to one significant figure)