If the acceleration is increasing, will the velocity also increase in every case?
If the acceleration is increasing, will the velocity also increase in every case?
Sure, as long as acceleration is positive, velocity increases, even if acceleration is decreasing (as long as it doesn't reach zero).
Likewise, as long as acceleration is negative, velocity decreases even if acceleration is increasing.
•Acceleration is the rate of change of velocity defined by a=dv/dta=dv/dt, so even if acceleration is decreasing as long as it is positive it velocity would increase. So if for example at time t=0t=0 we have that a=2m/sec2a=2m/sec2 which means that every second the velocity increases by 2 m/sec , and then say at time t=1t=1 we have a=1m/sec2a=1m/sec2 i.e da/dt<0da/dt<0 we still have that the velocity would increase by 1m/sec1m/sec
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Suppose a car driving in reverse direction slows down. If it was going at 20 meters per second and slows down to 10 meters per second in 10 seconds the speed is decreasing. Since it is moving in reverse direction its initial velocity was -20 meters per second and its final velocity is -10 meters per second hence velocity increases from -20 to -10 meters per second.
Since Acceleration is change in velocity per unit time, here it is 20/10 i.e. 2 meters per second squared
So it is possible.
Sure, as long as acceleration is positive, velocity increases, even if acceleration is decreasing (as long as it doesn't reach zero).
Likewise, as long as acceleration is negative, velocity decreases even if acceleration is increasing.
•Acceleration is the rate of change of velocity defined by a=dv/dta=dv/dt, so even if acceleration is decreasing as long as it is positive it velocity would increase. So if for example at time t=0t=0 we have that a=2m/sec2a=2m/sec2 which means that every second the velocity increases by 2 m/sec , and then say at time t=1t=1 we have a=1m/sec2a=1m/sec2 i.e da/dt<0da/dt<0 we still have that the velocity would increase by 1m/sec1m/sec
•
Suppose a car driving in reverse direction slows down. If it was going at 20 meters per second and slows down to 10 meters per second in 10 seconds the speed is decreasing. Since it is moving in reverse direction its initial velocity was -20 meters per second and its final velocity is -10 meters per second hence velocity increases from -20 to -10 meters per second.
Since Acceleration is change in velocity per unit time, here it is 20/10 i.e. 2 meters per second squared
So it is possible.
