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At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.70 m/s2. At the same instant a truck, traveling with a constant speed of 9.50 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck

Sagot :

lublana

Answer:

66.85 m

Explanation:

We are given that

Acceleration ,a=[tex]2.7m/s^2[/tex]

Speed of truck, v=9.5 m/s

We have to find the distance beyond which the traffic signal will the automobile overtake the truck.

Initial speed of automobile, u=0

We know that

[tex]s=ut+\frac{1}{2}at^2[/tex]

Using the formula

[tex]s=0+\frac{1}{2}(27)t^2=\frac{27}{2}t^2[/tex]

For constant speed

Acceleration, a=0

Again

[tex]s=vt+0=9.5t[/tex]

[tex]9.5t=\frac{27}{2}t^2[/tex]

[tex]t=\frac{9.5\times 2}{2.7}=7.037s[/tex]

Substitute the value of t

[tex]x=9.5(7.037)=66.85m[/tex]

Hence, the distance beyond which the traffic signal will the automobile overtake the truck=66.85 m

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