WHat is the displacement of a car that starts at 10m/s east and accelerates at 3m/s west for 2s
its not, it is 14 m east, the above answer is incorrect.
Well, imagine the car is in a race against itself - going east at 10 m/s and west at 3 m/s. It's like it can't decide which direction it really wants to go! As the car accelerates west for 2 seconds, it's like it's trying to pull off a cool dance move, but ends up doing the electric slide backwards. So, the displacement of the car would be the distance it traveled in that time, which is given by the formula: displacement = initial velocity * time + 1/2 * acceleration * time^2. Since the car is changing direction, we need to consider the signs of the velocities and acceleration.
First, let's calculate the displacement for the car moving east:
displacement_east = (10 m/s)* (2 s) + 0.5 * 0 * (2 s)^2 = 20 m
Next, let's calculate the displacement for the car moving west:
displacement_west = (-3 m/s) * (2 s) + 0.5 * (-3 m/s^2) * (2 s)^2 = -6 m
Finally, we can find the total displacement by adding the displacements in each direction:
total displacement = displacement_east + displacement_west
total displacement = 20 m + (-6 m)
total displacement = 14 m
So, the car would have a total displacement of 14 meters, in the direction of the initial velocity (east). Isn't it funny how a car can end up going forwards and backwards at the same time? It's like they're trying to mess with our minds!
To calculate the displacement of the car, we need to consider its initial velocity, acceleration, and the time for which the car accelerates.
For this problem:
Initial velocity (u) = 10 m/s east (positive direction)
Acceleration (a) = -3 m/s^2 west (negative direction)
Time (t) = 2 seconds
First, we need to find the final velocity (v) after the given time period using the formula:
v = u + at
Substituting the given values:
v = 10 m/s + (-3 m/s^2) * 2 sec
v = 10 m/s - 6 m/s
v = 4 m/s east
Next, we can use another formula to calculate the displacement (s) of the car:
s = ut + (1/2)at^2
Substituting the given values:
s = (10 m/s * 2 sec) + (1/2) * (-3 m/s^2) * (2 sec)^2
s = 20 m + (1/2) * (-3 m/s^2) * 4 sec^2
s = 20 m + (-6 m/s^2) * 4 sec^2
s = 20 m + (-6 m/s^2) * 16 sec^2
s = 20 m - 96 m
s = -76 m
Therefore, the displacement of the car is -76 meters. The negative sign indicates that the car has moved 76 meters west from its initial position.