Question

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead (from rest) with a constant acceleration of 1.4 m/s². At the same instant, a truck traveling with a constant speed of 39.5 mph passes the car.(a) Convert the truck’s speed from miles per hour to meters per second m/s. 1 mile = 1609 m, 1 hour = 60 minites, and 1 minute = 60 seconds. Keep 2 decimal places.(b) How much time in seconds does it take the car to catch up with the truck? Keep 2 decimal places.(c) How far in meters beyond its starting point does the car catch up with the truck? Keep 2 decimal placesHow far in meters beyond the intersection (where the truck first passes the car) is the truck when it is caught up with by the car? Keep 2 decimal places.

Answer 1

Part a)

`v = 17.65 m/s`

Part b)

`t = 25.22 s`

Part c)

`d = 445.25 m`

Step-by-step explanation:

Part a)

Speed of the truck is given as

`v = 39.5 mph`

also we know that

1 mile = 1609 m

1 h = 3600 s

now we have

`v = 39.5 * (1609)/(3600)`

`v = 17.65 m/s`

Part b)

Now if car catches the truck after time "t"

so the distance moved by car and truck will be same in this time

`(1)/(2)at^2 = v t`

`(1)/(2)1.4 t^2 = 17.65 t`

`t = 25.22 s`

Part c)

Distance moved by the car in the same time

`d = (1)/(2)at^2`

`d = (1)/(2)(1.4)(25.22^2)`

`d = 445.25 m`