A 10-kg block which starts at rest, begins sliding after being pushed by a constant force F of 15N. The time in seconds it takes for the block to reach 20 m/s is most nearly.
We know that F = m*a. If we plug in the force and mass values we can obtain the acceleration of the block:
$$15 = 10 * a => a = 15/10 = 3/2 = 1.5 m/s^2$$
We can integrate acceleration with respect to time to find velocity:
$$v = inta*dt = a*t + C$$
C is the initial velocity, which we know is 0 since the block starts at rest. Now we plug in the final velocity and solve for time.
$$20 m/s = a * t$$
$$t = 20/1.5 ~~ 13.33 s$$
The position of a particle that traverses a straight line is expressed as $$x(t)=t^3+2t^2-t+10$$, where x is in feet and t in seconds. What is the acceleration (ft/$$sec^2$$) of the particle when the velocity is zero?
The distance of a particle traveling on a straight line from point A is $$s=10t^2+t^3$$. The rate of change of acceleration at time $$t=4$$ is:
A tractor with a mass of 2,300 kg is traveling at 10 m/s. At time t = 0, the driver pulls the emergency brake and the tractor begins to slide. The properties of the relevant materials, are shown:
Material 1 | Material 2 | Static Friction | Kinetic Friction |
Rubber | Asphalt | 0.9 | 0.4 |
At t = 3, the speed (m/s) of the tractor is most nearly:
A sea vessel accelerates at a rate of $$22\ ft//sec^2$$. The vessel travels 140 ft while its speed changes to 70 ft/sec. The initial velocity (ft/sec) was most nearly: