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The acceleration of a particle is defined by the relation a
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- The position of a particle as a function of time t, is given by x(t) = at +bt² - ct³ where a, b and care constants. When the particle attains zero acceleration, then its velocity will be? A B с D a+ E + a+ a+ b² 4c b² 2c b² 3carrow_forwardStarting from x= 0 with no initial velocity, a particle is given an acceleration where a and v are expressed in ft/s2 and ft/s, respectively. Determine (a) the position of the particle when v= 3 ft/s, (b) the speed and acceleration of the particle when x= 4 ft.arrow_forwardplease answer the question as soon as possiblearrow_forward
- The position of a particle moving along a straight line is defined by the relation x = t3 - 6t2-15t + 40, where x is expressed in feet and t in seconds. Determine (a) the time at which the velocity is zero, (b) the position and distance traveled by the particle at that time, (C) the acceleration of the particle at that time,arrow_forwardquestionarrow_forwardEx.5.2 The position of a particle which moves along a straight line is defined by the relation x = t3 - 6t2 -15t + 40, where x is expressed in m and t in sec. Determine (a) the time at which the velocity will be zero, (b) the position and distance traveled by the particle at that time, (c) the acceleration of the particle at that time, d) the distance traveled by the particle from t= 4 s to t = 6 s. %3Darrow_forward
- A muzzle-loading rifle fires 22LR bullets such that as they travel down the barrel of the rifle their speed is given by v = (-5.25 x 1o')t? + (2.40 x 10')t, where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero. (a) Determine the acceleration (in m/s2) and position (in m) of the bullet as a function of time when the bullet is in the barrel. (Use the following as necessary: t. Round all numerical coefficients to at least three significant figures. Do not include units in your answers. Assume that the position of the bullet at t = 0 is zero.) a(t) = m/s2 x(t) = m (b) Determine the length of time the bullet is accelerated (in s). 2.3*10**-3 (c) Find the speed at which the bullet leaves the barrel (in m/s). m/s (d) What is the length of the barrel (in m)? marrow_forwardThe acceleration of a particle moving horizontally under rectilinear motion is defined by the relation a=9.4t2-4.6t where a is in ft/s2 and t is in s. Initially, the particle is moving at 6ft/s and started at x=9.6 ft. Determine the position of the particle at t=4.4s. Round off only on the final answer expressed in 3 decimals. Indicate appropriate units.arrow_forwarda_av = 3.9051 m/s^2arrow_forward
- t3 – 2t2 + 7 3. The motion of the particle along a straight line is governed by the relation a = where a is the acceleration in m/s² and t is the time in seconds. At time t = A second, the velocity of the particle is v m/s and the displacement is d m. Calculate the displacement, velocity and acceleration at timet = 2 seconds. - A = 1.476 second %3D 14.764 .m/s V = d = 218arrow_forward3) Two particles, A & B, move along parallel rectilinear paths. At t=0 the particles are directly opposite one another. Particle A moves according to SA = 12t² - 4t³ inches and particle B moves with a constant speed of 12 inches/ second. (a) Determine the relative position of A with respect to B at t = 1 second. (b) Determine the relative velocity of A with respect to B at t = 1 second. ANS. SA/B = -4 inches VA/B = 0 inches/secarrow_forward1(a) The displacement of a particle is given by s = 4t3 - 46t2 + 95t - 37 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 8 seconds of motion. After you have made the plots, answer the questions.arrow_forward
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