A particle moving in the x-y plane has a velocity v = 10.55i + 2.41j m/s at a certain instant. If the particle then encounters a constant acceleration a = 0.89j m/s², determine the amount of time which must pass before the direction of the tangent to the trajectory of the particle has been altered by 27°. Answer: t =
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- A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a stone with velocity v0 = 17 m/s at an angle θ = 27 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position. With what speed, vf in meters per second, does the stone strike the ground?Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) : c = 0.120 m/s², and d = 1.02 m. (a) Calculate the average velocity during the time interval from t = 2.10 s to t = 3.85 s. V = m/s (b) Determine the velocity at t = 2.10 s. m/s = at + b and y(t) = ct² + d, where a = 1.80 m/s, b = Determine the speed at t = 2.10 s. m/s 1.20 m,The position of a particle is r(t) = (5.0t2î – 4.0j + 6.0t³k) m. (a) What is the velocity of the particle at 0 s and at 1.0 s (in m/s)? (Express your answers in vector form.) v(0 s) m/s v(1.0 s) m/s (b) What is the average velocity between 0 s and 1.0 s (in m/s)? (Express your answer in vector form.) Vavg m/s
- At t = 0 a particle at the origin has a velocity of 15.1 m/s at 36° above the horizontal x axis. At t = 5.00 s it is at x = 21.0 m and y = 35.0 m and its velocity is 30.0 m/s at 53° above the horizontal. Find: (a) its average velocity; (b) its average accelerationAn object moves on xy plane according to the equation 7 = 20 cos(3t) î + (1,5t + 3,5t2)j. Determine its position at t = 0. Find its average velocity and average acceleration between t = 2s and t = 5s.A computer model displays the motion of a particle on a coordinate system in real time. At time t = 0, the particle is at the origin of the coordinate system and has velocity components vx = 0 and vy = 6.8 m/s. The particle has acceleration components of ax = −4.8 m/s2 and ay = 0. (a) What are the x and y positions of the particle at t = 4.0 s?(b) What are velocity components of the particle at t = 4.0 s?(c) How does the speed of the particle change from t = 0 to t = 4.0 s?
- The vector position of a particle varies in time according to the expression F(t)=(1.41 t + 1.72)i +(0.224t2 + 1.11)J where r is in meters and t is in seconds. Find the speed of the particle in m/s at 2.58 s.An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.A computer model displays the motion of a particle on a coordinate system in real time. At time t = 0, the particle is at the origin of the coordinate system and has velocity components vx = 10.0 m/s and vy = 0 m/s. The particle has acceleration components of ax = 0 and ay = 3.0 m/s^2. (a) What are the x and y positions of the particle at t = 6.0 s? (b) What are velocity components of the particle at t = 6.0 s? (c) What is the speed of the particle at t = 6.0 s?
- A snowmobile is originally at the point with position vector 30.5 m at 95.0° counterclockwise from the x-axis, moving with velocity 4.89 m/s at 40.0°. It moves with a constant acceleration 1.72 m/s2 at 200°. After 5.00 s have elapsed, find the following. (Express your answers in vector form.) (a) its velocity vector. (b) its position vector.A computer model displays the motion of a particle on a coordinate system in real time. At time t = 0, the particle is at the origin of the coordinate system and has velocity components vx = 0 and vy = 7.2 m/s. The particle has acceleration components of ax = −3.2 m/s2 and ay = 0. (a) What are the x and y positions of the particle, in meters, at t = 4.5 s? x = ? m y = ? m (b) What are velocity components of the particle, in m/s, at t = 4.5 s? vx = ? m/s vy = ? m/s (c) How does the speed of the particle change from t = 0 to t = 4.5 s? a) The particle's speed remains constant. b) The particle's speed increases and then decreases with time. c) The particle's speed decreases with time. d) The particle's speed increases with time.A particle confined to the xy-plane is in uniform circular motion around the origin. The x- and y-coordinates of the particle vary with time as follows: x(t) = r sin(cot) y(t) = r cos(cot). where >= 2.60 m and c = 2.15 s-¹. What are the x- and y-components of the particle's acceleration at an instant when x = 1.00 m and y = 2.40 m. Give your answers by entering numbers into the empty boxes below. ax || || X x² ms ms-2.