Determine the velocity and acceleration if the displacement as a function of time is $s=3t^2+4$
See images:
The acceleration of a particle is given by $a=4-6t$. The velocity is 2m/s when t=1s and the initial displacement is 6m.
A particle is moving along a straight line with the acceleration $a=(12t-3t^{1/2})ft/s^2$, where t is in seconds. Determine the velocity and the position of the particle as a function of time. When t=0, v=0 and s=15ft.
The acceleration of a particle travelling along a straight line is $a=k/v$, where $k$ is a constant. If $s=0\text{, }v=v_0\text{, when }t=0$, determine the velocity of the particle as a function of time.
A particle travels along a straight line with a velocity $v = (12 – 3t^2)m/s$, where t is in seconds. When t = 1s, the particle is located 10m to the left of the origin. Determine the acceleration when t = 4s and identify whether the body is decelerating or accelerating. Also determine the displacement from t = 0 to t = 10s, and the distance the particle travels during this time period. After which, calculate the average speed and average velocity.
A car starting from rest is moving at constant acceleration until it reaches a final velocity of 19m/s after travelling a distance of 153.2m. Calculate the acceleration and the required time.
A jumbo jet needs to reach a speed of 360km/h on the runway for takeoff. Assuming a constant acceleration and a runway 1.8km long, what minimum acceleration from rest is required? Express your answer in m/s2.
A sprinter in the 100-m dash accelerates from rest to a top speed at 2.8m/s2 and maintains the top speed to the end of the dash. a) What time elapsed and b) what distance did the sprinter cover during the acceleration phase if the total time taken in the dash was 12.2 seconds?
An auto A is moving at 20fps and accelerating at 5fps2 to overtake an auto B which is 384ft ahead. If auto B is moving at 60fps and decelerating at 3fps2, how soon will A pass B?
A motorcycle is stopped by the side of the road when a car passes at 50mi/h. Twenty seconds later, the motorcycle starts chasing the car. Assume that the motorcycle accelerates at 8ft/s2 until it reaches 60mi/h and then travels at a constant speed. Find the amount of time it will take for the motorcycle to overtake the car and the total distance traveled by the motorcycle in that time.
In travelling a distance of 3km between points A and D, a car is driven at 100km/h from A to B for t seconds and at 60km/h from C to D also for t seconds. If the brakes are applied for four seconds between B and C to give the car a uniform deceleration, calculate t and the distance s between A and B, in seconds and kilometers, respectively.
