A car and a truck starts from same point along same direction ,car with initial speed 2m/s and acceleration 2 m/s^2 and truck with a constant speed 20 m/s ,find the time after which car will overtake the truck
To find the time after which the car will overtake the truck, we need to determine when their positions will be equal.
Let's denote the time at which the car and the truck meet as 't'. During this time, the car will have covered a certain distance and the truck will have covered the same distance.
Let's calculate the distance covered by each vehicle after time 't'.
The distance covered by the car can be calculated using the equation of motion:
s_car = u_car * t + 0.5 * a_car * t^2,
where:
- s_car is the distance covered by the car,
- u_car is the initial speed of the car (2 m/s),
- a_car is the acceleration of the car (2 m/s^2),
- t is the time.
The distance covered by the truck can be calculated using the equation:
s_truck = u_truck * t,
where:
- s_truck is the distance covered by the truck,
- u_truck is the constant speed of the truck (20 m/s).
Since both vehicles meet at the same distance,
s_car = s_truck.
Substituting the equations for s_car and s_truck, we have:
u_car * t + 0.5 * a_car * t^2 = u_truck * t.
Rearranging the equation, we get:
0.5 * a_car * t^2 + (u_car - u_truck) * t = 0.
This is a quadratic equation in terms of 't'. We can solve it by substituting the values:
a_car = 2 m/s^2,
u_car = 2 m/s,
u_truck = 20 m/s.
Plugging these values into the equation, we have:
0.5 * 2 * t^2 + (2 - 20) * t = 0.
Simplifying the equation, we get:
t^2 - 18t = 0.
Factorizing 't' from the equation, we have:
t * (t - 18) = 0.
This equation has two solutions: t = 0 and t = 18.
However, t = 0 represents the time of starting from the same point, so it is not the desired solution.
Therefore, the car will overtake the truck after 18 seconds.
To find the time after which the car will overtake the truck, we need to determine when their positions will be equal.
Let's consider the following variables:
- t: time (in seconds)
- d_car: distance covered by the car (in meters)
- d_truck: distance covered by the truck (in meters)
First, we'll determine the equations for the distance covered by each vehicle at time t.
For the car:
Using the equation: d_car = initial_velocity * t + 0.5 * acceleration * t^2
Substituting the given values: d_car = 2t + 0.5 * 2 * t^2
Simplifying, we get: d_car = 2t + t^2
For the truck:
Since the truck is moving with a constant speed of 20 m/s, the equation is simpler:
d_truck = truck_speed * t
Substituting the given values: d_truck = 20t
To find the time when the car overtakes the truck, we need to solve the equation d_car = d_truck.
Substituting the equations for d_car and d_truck:
2t + t^2 = 20t
Rearranging terms:
t^2 + 2t - 20t = 0
Simplifying:
t^2 - 18t = 0
Factoring out t:
t(t - 18) = 0
Therefore, t = 0 or t = 18.
The time t = 0 is when both vehicles start, so it is not relevant to our question.
Thus, the car will overtake the truck after 18 seconds.
d1 = 2t^2 + 2t
d2 = 20t
the time of overtaking is when d1 = d2
2t^2 + 2t = 20t
t^2 - 9t = 0
t(t - 9) = 0
interpret this equation, and find the answer to your question from it.
d = vt + 1/2 at^2
so d1 = 2t + 1t^2