the driver of a truck going 50 mph applies the brakes giving the truck a deceleration of 4.5 m/s^2 how long will it take the truck to come to a complete stop what distance will it cover
now wait a minute, this is too much like the last one. You try for a while. I already know how.
To find the time it takes for the truck to come to a complete stop, we can use the formula:
Time = Change in velocity / Acceleration
In this case, the initial velocity of the truck is 50 mph, which we need to convert to meters per second (m/s). We know that 1 mph is equal to 0.44704 m/s.
So, the initial velocity of the truck can be calculated as:
Initial velocity = 50 mph * 0.44704 m/s = 22.352 m/s
Next, we know the truck's deceleration is 4.5 m/s^2.
Plugging these values into the formula, we get:
Time = (0 m/s - 22.352 m/s) / (-4.5 m/s^2)
Note that we take the negative sign for the acceleration because it represents deceleration.
Simplifying this, we have:
Time = -22.352 m/s / -4.5 m/s^2
The negative signs cancel out, so the equation becomes:
Time = 22.352 m/s / 4.5 m/s^2
Calculating the value, we find:
Time = 4.967 seconds (rounded to three decimal places)
Hence, it will take approximately 4.967 seconds for the truck to come to a complete stop.
To find the distance the truck will cover, we can use the following formula:
Distance = (Initial velocity)^2 / (2 * Acceleration)
Plugging in the values, we have:
Distance = (22.352 m/s)^2 / (2 * (-4.5 m/s^2))
Notice that we use the negative sign for the acceleration, as it represents deceleration.
Simplifying, we get:
Distance = 497.3656 m^2/s^2 / -9 m/s^2
Distance = -55.2628 m
Therefore, the truck will cover approximately 55.2628 meters before coming to a complete stop.