The velocity of a body varies as v = 2t^2 - 4t + 6 (m/s). The acceleration when the body attains its minimum velocity is:

A stone is thrown vertically upward with initial velocity 19.6 m/s. After how much time will it return to the starting point? (g = 9.8 m/s^2)

A particle moves along x-axis. Its position varies with time as x = 5t - 5t^2 (m). The velocity when it returns to the initial position is:

A projectile can have the same range R for two angles of projection. If t_1 and t_2 are the times of flight in the two cases, then R is proportional to:

A car starts from rest and accelerates uniformly for 10 s. It then moves at constant velocity for 30 s and is then brought to rest with uniform deceleration in 5 s. The total distance is 1000 m. Find the maximum velocity. <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 380 180" style="max-width:380px;margin:0.5em auto;display:block;"> <title>Trapezoidal v-t graph for multi-phase motion</title> <rect width="380" height="180" fill="#faf9f5" rx="6"/> <defs><marker id="ah-q76" markerWidth="8" markerHeight="6" refX="8" refY="3" orient="auto"><polygon points="0 0, 8 3, 0 6" fill="#14140f"/></marker></defs> <line x1="40" y1="150" x2="360" y2="150" stroke="#14140f" stroke-width="1.5" marker-end="url(#ah-q76)"/> <line x1="40" y1="150" x2="40" y2="15" stroke="#14140f" stroke-width="1.5" marker-end="url(#ah-q76)"/> <text x="350" y="168" font-size="10" font-family="sans-serif" fill="#14140f">t(s)</text> <text x="20" y="20" font-size="10" font-family="sans-serif" fill="#14140f">v</text> <polygon points="40,150 110,40 290,40 330,150" fill="#c6613f" fill-opacity="0.12" stroke="#c6613f" stroke-width="2"/> <text x="20" y="44" font-size="10" font-family="sans-serif" fill="#14140f">v_max</text> <text x="70" y="168" font-size="9" font-family="sans-serif" fill="#14140f">10</text> <text x="195" y="168" font-size="9" font-family="sans-serif" fill="#14140f">40</text> <text x="320" y="168" font-size="9" font-family="sans-serif" fill="#14140f">45</text> <text x="150" y="110" font-size="10" font-family="sans-serif" fill="#788c5d">Area = 1000 m</text> </svg>