A truck starts from the rest and moves with a accelaration 1.5m/s^2 ,at the same time a car which is 150m behind the truck starts from the rest with an accelaration of 2m/sec^2. Find the time which the car will overtake the truck and the distance travel.

Question

A truck starts from the rest and moves with a accelaration 1.5m/s^2 ,at the same time a car which is 150m behind the truck starts from the rest with an accelaration of 2m/sec^2. Find the time which the car will overtake the truck and the distance travel.

Answer 1

To find the time at which the car overtakes the truck, we can start by determining when the two vehicles have traveled the same distance. Let's call this distance "d".

We know that the car starts 150m behind the truck, so we can express the initial position of the car as "d - 150", where "d" is the distance traveled by both vehicles.

Let's calculate the distance traveled by the truck at time "t" using the equation:

distance_truck = 0.5 * acceleration_truck * t^2

And the distance traveled by the car at time "t" using the equation:

distance_car = 0.5 * acceleration_car * t^2

Now, the distance traveled by the car is the initial position of the car plus the distance traveled by the car itself:

distance_car = (d - 150) + (0.5 * acceleration_car * t^2)

Since the two vehicles have the same distance at the moment of overtaking, we can set the two distance equations equal to each other:

0.5 * acceleration_truck * t^2 = (d - 150) + (0.5 * acceleration_car * t^2)

Simplifying the equation:

0.5 * acceleration_truck * t^2 - 0.5 * acceleration_car * t^2 = d - 150

0.5 * (acceleration_truck - acceleration_car) * t^2 = d - 150

Now, we can solve for the time, "t":

t^2 = (2 * (d - 150)) / (acceleration_truck - acceleration_car)

t = √((2 * (d - 150)) / (acceleration_truck - acceleration_car))

To find the distance traveled at the time of overtaking, we can substitute the value of "t" back into either of the distance equations. Let's use the truck's distance equation:

distance_truck = 0.5 * acceleration_truck * t^2

Remember that the distance traveled by both vehicles will be the same:

d = distance_truck

So, the distance traveled by the truck at the time of overtaking is:

d = 0.5 * acceleration_truck * t^2

Now, we have derived the equation to find the time of overtaking "t" and the distance traveled by both vehicles "d". You can substitute the given values for acceleration_truck, acceleration_car, and solve for "t". Once you have the value of "t", substitute it back into the equation for "d" to find the distance traveled.

Answer 2

Dc = Dt + 150

0.5a2*t^2 = 0.5a1*t^2. + 150.
a1 = 1.5 m/s^2.
a2 = 2 m/s^2.
t = ?.

Dc = 0.5a2*t^2 =