Answer:
Car velocity when crossing checkpoint = 60 m/s
Explanation:
For an object traveling at an acceleration of a m/s², with an initial velocity of u m/s the displacement at time = t secs is given in meters by the equation
[tex]\displaystyle d=ut+\frac{1}{2}at^{2}[/tex]
Here we are given displacement, and time but not acceleration and initial velocity : d = 225 meters, t = 5 seconds
Let's find an equation relating u and a in terms of d and using data given
Switching sides we get
[tex]ut+\frac{1}{2}at^{2}=d[/tex]
Substituting values for t = 5, d = 225 we get
[tex]5u+\frac{1}{2}a.25=225[/tex]
Multiplying both sides by 2 yields
[tex]10u+25a=450\;\;\; ...... (1)[/tex]
We also have the formula:
[tex]\displaystyle a=\frac{{v-u}}{t}[/tex]
where v is the current velocity and u the initial velocity
So
[tex]\displaystyle a=\frac{30-u}{5}[/tex]
[tex]u+5a=30\;\;...... (2)[/tex]
Multiply equation (2) by 5 and subtract from (1) to eliminate the a terms and solve for u
[tex]\displaystyle 10u+25a-5u-25a=450-150\\\\5u=300\\\\u=60m/s\\\\\textsf{which is the speed at which the car passes the checkpoint}\\[/tex]